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An IntroductIon to

Transport Phenomena in Materials Engineering second edItIon

DaviD R. GaskEll

Contents  xi

List of Symbols   xvii 1  Engineering Units and Pressure in Static Fluids   1 1.1  1.2  1.3  1.4  1.5  1.6 

Origins of Engineering Units   1 Concept of Pressure   5 Measurement of Pressure   11 Pressure in Incompressible Fluids   15 Buoyancy   21 Summary   26 Problems   27

2 Momentum Transport and Laminar Flow of Newtonian Fluids   30 2.1  2.2  2.3  2.4  2.5  2.6  2.7 

Introduction   30 Newton’s Lax of Viscosity   32 Conservation of Momentum in Steady-State Flow   36 Fluid Flow Between Two Flat Parallel Plates   40 Fluid Flow down in Inclined Plane   48 Fluid Flow in a Vertical Cylindrical Tube   53 Capillary Flowmeter   65 xi

xii  Contents

2.8  Fluid Flow in an Annulus   69 2.9  Mean Residence Time   76 2.10  Calculation of Viscosity from the Kinetic Theory of Gases   78 2.11  Viscosities of Liquid Metals   90 2.12  Summary   96 Problems   98

3 Equations of Continuity and Conservation of Momentum and Fluid Flow Past Submerged Objects   102 3.1  Introduction   102 3.2  Equation of Continuity   102 3.3  Conservation of Momentum   104 3.4 Navier-Stokes Equation for Fluids of Constant Density and Viscosity   108 3.5  Fluid Flow over a Horizontal Flat Plane   115 3.6 Approximate Integral Method in Obtaining Boundary Layer Thickness   117 3.7  Creeping Flow past a Sphere   125 3.8  Summary   132 Problems   133

4 Turbelent Flow   135 4.1  Introduction   135 4.2  Graphical Representation of Fluid Flow   139 4.3  Friction Factor and Turbulent Flow in Cylindrical Pipes   141 4.4 Flow Over a Flat Plate   153 4.5  Flow Past a Submerged Sphere   160 4.6 Flow Past a Submerged Cylinder   163 4.7  Flow Through Packed Beds   167 4.8  Fluidized Beds   175 4.9  Summary   180 Problems   181

5 Mechanical Energy Balance and Its Application to Fluid Flow   185 5.1  Introduction   185 5.2  Bernoulli’s Equation   185

Contents  xiii

5.3  Friction Loss, Ef   188 5.4 Influence of Bends, Fittings, and Changes in the Pipe Radius   190 5.5  Concept of Head   203 5.6 Fluid Flow in an Open Channel   205 5.7  Drainage from a Vessel   207 5.8  Emptying a Vessel by Discharge Through an Orifice   209 5.9  Drainage of a Vessel Using a Drainage Tube   213 5.10  Emptying a Vessel by Drainage Through a Drainage Tube   215 5.11  Bernoulli Equation for Flow of Compressible Fluids   219 5.12  Pilot Tube   221 5.13  Orifice Plate   225 5.14  Summary   228 Problems   229

6 Transport of Heat by Conduction   235 6.1  Introduction   235 6.2  Fourier’s Law and Newton’s Law   236 6.3  Conduction   238 6.4 Conduction in Heat Sources   256 6.5  Thermal Conductivity and the Kinetic Theory of Gases   267 6.6 General Heat Conduction Equation   274 6.7  Conduction of Heat at Steady State in Two Dimensions    278 6.8  Summary   289 Problems   290

7 Transport of Heat by Convection   295 7.1  Introduction   295 7.2 Heat Transfer by Forced Convection from a Horizontal Flat Plate at a Uniform Constant Temperature   295 7.3 Heat Transfer from a Horizontal Flat Plate with Uniform Heat Flux Along the Plate   315 7.4 Heat Transfer During Fluid Flow in Cylindrical Pipes   317 7.5 Energy Balance in Heat Transfer by Convection Between a Cylindrical Pipe and a Flowing Fluid   322 7.6 Heat Transfer by Forced Convection from Horizontal Cylinders   331 7.7 Heat Transfer by Forced Convection from a Sphere   334 7.8  General Energy Equation   335 7.9  Heat Transfer from a Vertical Plate by Natural Convection   346

xiv  Contents

7.10  Heat Transfer from Cylinders by Natural Convection   358 7.11  Summary   360 Problems   361

8 Transient Heat Flow   365 8.1  Introduction   365 8.2  Lumped Capacitance Method; Newtonian Cooling   365 8.3  Non-Newtonian Cooling in Semi-infinite Systems   373 8.4 Non-Newtonian Cooling in a One-Dimensional Finite Systems   382 8.5 Non-Newtonian Cooling in a Two-Dimensional Finite Systems   394 8.6 Solidification of Metal Castings   401 8.7  Summary   416 Problems   416

9 Heat Transport by Thermal Radiation   421 9.1  Introduction   421 9.2  Intensity and Emissive Power   423 9.3  Blackbody Radiation   427 9.4 Emissivity   431 9.5 Absorptivity, Reflectivity, and Transmissivity   436 9.6 Kirchhoff’s Law and the Hohlraum   437 9.7 Radiation Exchange Between Surfaces   439 9.8 Radiation Exchange Between Blackbodies   450 9.9 Radiation Exchange Between Diffuse-Gray Surfaces   453 9.10 Electric Analogy   458 9.11 Radiation Shields   460 9.12 Reradiating Surface   463 9.13 Heat Transfer from a Surface by Convection and Radiation   466 9.14  Summary   471 Problems   472

10 Mass Transport by Diffusion in the Solid State   476 10.1  Introduction   476 10.2  Atomic Diffusion as a Random-Walk Process   476 10.3  Fick ’s First Law of Diffusion   480

Contents  xv

10.4 One-Dimensional Non-Steady-State Diffusion in a Solid; Fick ’s Second Law of Diffusion   483 10.5 Infinite Diffusion Couple   489 10.6 One-Dimensional Diffusion in a Semi-infinite System Involving a Change of Phase   491 10.7 Steady-State Diffusion Through a Composite Wall   498 10.8 Diffusion in Substitutional Solid Solutions   502 10.9 Darken’s Analysis   502 10.10 Self-Diffusion Coefficient   506 10.11 Measurement of the Interdifussion Coefficient: Boltzmann– Matano Analysis   510 10.12 Influence of Temperature on the Diffusion Coefficient   514 10.13  Summary   518 Problems   520

11 Mass Transport in Fluids   522 11.1  Introduction   522 11.2  Mass and Molar Fluxes in a Fluid   522 11.3 Equations of Diffusion with Convection in a Binary Mixture A–B   524 11.4 One-Dimensional Transport in a Binary Mixture of Ideal Gases   527 11.5 Equimolar Counterdiffusion   528 11.6 One-Dimensional Steady-State Diffusion of Gas A Through Stationary Gas B   529 11.7 Sublimation of a Sphere into a Stationary Gas   536 11.8 Film Model   538 11.9 Catalytic Surface Reactions   539 11.10 Diffusion and Chemical Reaction in Stagnant Film   542 11.11 Mass Transfer at Large Fluxes and Large Concentrations   547 11.12 Influence of Mass Transport on Heat Transfer in Stagnant Film   550 11.13 Diffusion into a Falling Film of Liquid   553 11.14 Diffusion and the Kinetic Theory of Gases   560 11.15 Mass Transfer Coefficient and Concentration Boundary Layer on a Flat Plate   569 11.16 Approximate Integral Method   573 11.17 Mass Transfer by Free Convection   583 11.18 Simultaneous Heat and Mass Transfer: Evaporate Cooling   586 11.19 Chemical Reaction and Mass Transfer: Mixed Control   589 11.20 Dissolution of Pure Metal A in Liquid B: Mixed Control   593 11.21  Summary   596 Problems   598

xvi  Contents

12 Condensation and Boiling    601 12.1  12.2  12.3  12.4  12.5 

Introduction   601 Dimensionless Parameters in Boiling and Condensation   602 Modes of Boiling   603 Pool Boiling Correlations   606 Summary   612 Problems   612

Appendix A Elementary and Derived SI Units and Symbols   615 Appendix B Prefixes and Symbols for Multiples and Submultiples of SI Units   617 Appendix C Conversion from British and U.S. Units to SI Units   618 Appendix D Properties of Solid Metals   620 Appendix E Properties of Nonmetallic Solids   623 Appendix F Properties of Gases at 1 Atm Pressure   627 Appendix G Properties of Saturated Liquids   635 Appendix H Properties of Liquid Metals   639 Recommended Readings   642 Answers to Problems   643 Index   651

xvii

xviii  List of Symbols

List of Symbols  xix

xx  List of Symbols

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A n I n t ro d u c tI o n to

Transport Phenomena in Materials Engineering s e c ond edIt Ion, By David R. Gaskell This classic text on fluid flow, heat transfer, and mass transport has been brought up to date in this second edition. The author has added a chapter on “Boiling and Condensation” that expands and rounds out the book’s comprehensive coverage on transport phenomena. These new topics are particularly important to current research in renewable energy resources involving technologies such as windmills and solar panels. The book provides you and other materials science and engineering students and professionals with a clear yet thorough introduction to these important concepts. It balances the explanation of the fundamentals governing fluid flow and the transport of heat and mass with common applications of these fundamentals to specific systems existing in materials engineering. You will benefit from: • The use of familiar examples such as air and water to introduce the influences of properties and geometry on fluid flow. • An organization with sections dealing separately with fluid flow, heat transfer, and mass transport. This sequential structure allows the development of heat transport concepts to employ analogies of heat flow with fluid flow and the development of mass transport concepts to employ analogies with heat transport. • Ample high-quality graphs and figures throughout. • Key points presented in chapter summaries. • End of chapter exercises and solutions to selected problems. • An all new and improved comprehensive index. About the Author David r. Gaskell was born in Glasgow, Scotland and received B.Sc. degrees in metallurgy and technical chemistry from the University of Glasgow in 1962. From 1962 to 1964, he was employed as the Metallurgist with Laporte Chemical Ltd., a manufacturer of industrial chemicals, with two plants in England. He obtained his Ph.D. from McMaster University in 1967, and from 1967 to 1982 he was a professor of metallurgy, materials science and geology at the University of Pennsylvania. In 1982 he came to Purdue, where he has won five departmental teaching awards. He has taught a variety of courses dealing with materials properties, structures and processing, and he is the author of two texts, one on the thermodynamics of materials, which is in its sixth edition, and this book on transport phenomena in materials engineering, which is now in its second edition. His research interests include chemical and extraction metallurgy, thermodynamics, kinetics, transport phenomena and materials processing. ISBN: 978-1-60650-355-3

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